A high-pass filter will send along high frequency signals but block low frequencies. It can do so because the impedance, Xc<\/sub>, of a capacitor of capacitance C, at frequency f, is<\/p>\n Xc<\/sub>=1\/(2\u03c0fC)<\/p>\n At very high frequency, therefore, Xc<\/sub>\u22480<\/p>\n The total impedance, Z, of a resistor R and capacitor C in series is given by<\/p>\n Z=(R2<\/sup> + Xc<\/sub>2<\/sup>)0.5<\/sup><\/p>\n Therefore, with input voltage V, and instantaneous current i, Ohm’s Law gives<\/p>\n V=i(R2<\/sup> + Xc<\/sub>2<\/sup>)0.5<\/sup><\/p>\n The voltage across the resitor is<\/p>\n VR<\/sub>=iR<\/p>\n Therefore, the ratio of the voltage across the resistor to the source is<\/p>\n VR<\/sub>\/V = iR\/i(R2<\/sup> + Xc<\/sub>2<\/sup>)0.5<\/sup> = R\/(R2<\/sup> + Xc<\/sub>2<\/sup>)0.5<\/sup><\/p>\n As mentioned earlier, for high frequency, Xc<\/sub>\u22480, giving<\/p>\n VR<\/sub>\/V \u2248 R\/(R2<\/sup>)0.5<\/sup> = 1<\/p>\n With a high-pass filter, the maximum output voltage for a high frequency signal equals the input voltage.<\/p>\n Convention says that the critical frequency, fc<\/sub>, is that at which VR<\/sub>\/V = 1\/(2)0.5<\/sup> = 0.707, which occurs when Xc<\/sub> = R:<\/p>\n VR<\/sub>\/V = R\/(R2<\/sup> + Xc<\/sub>2<\/sup>)0.5<\/sup> = R\/(R2<\/sup> + R2<\/sup>)0.5<\/sup> = R\/(2R2<\/sup>)0.5<\/sup><\/p>\n which leads to<\/p>\n VR<\/sub>\/V = 1\/20.5<\/sup> = 0.707<\/p>\n Therefore, a high-pass filter will pass any frequency higher than the critical frequency fc<\/sub>, where fc<\/sub> is calculated from<\/p>\n Xc<\/sub> = R<\/p>\n 1\/(2\u03c0fc<\/sub>C) = R<\/p>\n 1 = 2\u03c0fc<\/sub>CR<\/p>\n 1\/(2\u03c0CR) = fc<\/sub><\/p>\n By that reasoning, a 10k\u2126 resistor, in series with a 12pF (picoFarad) capacitor, placed in series, should produce a high-pass filter with critical frequency fc<\/sub> = 1.3MHz. The output would be read across the resistor R.<\/p>\n Source:<\/p>\n www.electronics-tutorials.ws<\/a><\/p>\n ecee.colorado.edu<\/a><\/p>\n Serway, Raymond A. Physics for Scientists and Engineers<\/u> with modern physics. Toronto: Saunders College Publishing, 1986.<\/p>\n